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# Electronic properties

Undoped parent compounds of cuprates are electrical insulators. The effect of doping is illustrated in attached Fig. 1. [1]
The conventional band-theory prediction is represented in (a), from which one would expect to La$_2$CuO$_4$ to be metallic with a carrier density of one per Cu site. A more realistic picture is shown in (b), indicating the splitting by energy $U$ between the upper and lower Hubbard bands, with the O $2p$ bands in-between, resulting in a charge transfer gap of $\Delta\approx 2$ eV.

With doping, a rigid band picture would predict that the Fermi level would move down into the O $2p$ band, for hole doping as in (c), or up into the upper Hubbard band, for electron doping as in (d). Instead, experiment suggests that weight is transferred into new mid-gap states, as indicated in (e).

Core level spectroscopy shows that the band created upon doping has primarily Oxygen p-character. The concentration of free carriers can be extracted from the ac-conductivity measurements and from the Hall resistivity measurements. The detailed structure of the electronic states can be obtained from the Angular resolved photoemission (ARPES) or by observing quasiparticle interferences in Scanning Tunneling force microscopy (STM).

### References

1. S. Uchida, T. Ido, H. Takagi, T. Arima, and Y. Tokura, Phys. Rev. B 43, 7942 (1991).